{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computation of the `pi table` for the observation sequence [`low speed` (`t=1`), `high speed` (`t=2`), `low speed` (`t=3`)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# 0 = left\n",
    "# 1 = right\n",
    "pi_zero = np.array([0.8, 0.2])  # deduced from the `alpha_table`\n",
    "transition = np.array([[0.8, 0.4], [0.2, 0.6]])\n",
    "\n",
    "def pi(k):\n",
    "    if k == 0:\n",
    "        return pi_zero\n",
    "    return np.dot(transition, pi(k-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.8        0.2       ]\n",
      " [0.72       0.28      ]\n",
      " [0.688      0.312     ]\n",
      " [0.6752     0.3248    ]\n",
      " [0.67008    0.32992   ]\n",
      " [0.668032   0.331968  ]\n",
      " [0.6672128  0.3327872 ]\n",
      " [0.66688512 0.33311488]]\n"
     ]
    }
   ],
   "source": [
    "# collect values\n",
    "res = np.reshape(pi(0), (1, 2))\n",
    "for i in range(1, 8):\n",
    "    temp = np.reshape(pi(i), (1, 2))\n",
    "    res = np.concatenate((res, temp), axis=0)\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the change in the state distribution as the prediction horizon increases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "    \n",
    "fig = plt.figure(figsize=(12, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "plt.plot(res, c='k')\n",
    "\n",
    "scatter_l = plt.scatter(np.arange(res[:, 0].size), res[:, 0], s=200, c='g', label=r'$\\pi[leftLane, k]$')\n",
    "scatter_r = plt.scatter(np.arange(res[:, 1].size), res[:, 1], s=200, c='orange', label=r'$\\pi[rightLane, k]$')\n",
    "\n",
    "init_prob_right = 2/3\n",
    "init_prob_left = 1/3\n",
    "prior_l = plt.axhline(y=init_prob_right, c='g', linestyle=\"-.\", linewidth=3)\n",
    "prior_r = plt.axhline(y=init_prob_left, c='orange', linestyle=\"-.\", linewidth=3, label=r'$\\pi[rightLane, k]$')\n",
    "\n",
    "l0 = plt.legend([scatter_l, prior_l], [r'$\\pi[leftLane, k]$', r'$\\Prior[leftLane]$'], loc='upper right', prop={'size': 18})\n",
    "l2 = plt.legend([scatter_r, prior_r], [r'$\\pi[rightLane, k]$', r'$\\Prior[rightLane]$'], loc='lower right', prop={'size': 18})\n",
    "plt.gca().add_artist(l0)\n",
    "\n",
    "plt.grid()\n",
    "plt.ylim(0, 1)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "plt.xlabel(r'$\\ k$', fontsize=18, fontweight='bold')\n",
    "plt.ylabel(r'$\\pi[i, k]$', fontsize=18, fontweight='bold')\n",
    "fig.text(0.37, 0.95, r'$\\pi[rightLane, k]$', ha=\"center\", va=\"bottom\", size=\"medium\", color=\"g\", fontsize=23)\n",
    "fig.text(0.5, 0.95, \"and\", ha=\"center\", va=\"bottom\", size=\"medium\", fontsize=23)\n",
    "fig.text(0.62,0.95,'$\\pi[leftLane, k]$', ha=\"center\", va=\"bottom\", size=\"medium\",color=\"orange\", fontsize=23)\n",
    "\n",
    "fig.savefig('docs/pi_of_k.svg', format='svg', dpi=1500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
